Question: $\dfrac{ 9c + 7d }{ 10 } = \dfrac{ 6c - 2e }{ 10 }$ Solve for $c$.
Solution: Notice that the left- and right- denominators are the same $\dfrac{ 9c + 7d }{ {10} } = \dfrac{ 6c - 2e }{ {10} }$ So we can multiply both sides by $10$ ${10} \cdot \dfrac{ 9c + 7d }{ {10} } = {10} \cdot \dfrac{ 6c - 2e }{ {10} }$ $9c + 7d = 6c - 2e $ Combine $c$ terms on the left. ${9c} + 7d = {6c} - 2e$ ${3c} + 7d = -2e$ Move the $d$ term to the right. $3c + {7d} = -2e$ $3c = -2e - {7d}$ Isolate $c$ by dividing both sides by its coefficient. ${3}c = -2e - 7d$ $c = \dfrac{ -2e - 7d }{ {3} }$